Given $A=\{0,1,2,3\}$ and $B=[-\pi,\pi]$, is $A\cup B=B$ true? $\Bbb{Z}\cap B=\{−3,−2,−1,0,1,2,3\}$? (and three others)

Question

I was given these two sets of numbers:

$$A=\{0,1,2,3\}\qquad B=[−π,π]\;\;\text{(closed interval)}$$

Are these two correct? (I think yes.)

1. $A\cup B=B$
2. $\Bbb{Z}\cap B=\{−3,−2,−1,0,1,2,3\}$

I was also given these (in my opinion, they are false):

3. $(\Bbb{Z}−A)\subset\Bbb{N}$
4. $\Bbb{N}\cap B=A$
5. $A\cup B=A$

$\Bbb{Z}$ - integers, $\Bbb{N}$ - natural numbers (without $0$)

Thx